Khan.scratchpad.disable(); For every level Daniel completes in his favorite game, he earns $550$ points. Daniel already has $140$ points in the game and wants to end up with at least $3100$ points before he goes to bed. What is the minimum number of complete levels that Daniel needs to complete to reach his goal?
Explanation: To solve this, let's set up an expression to show how many points Daniel will have after each level. Number of points $=$ $ $ Levels completed $\times$ Points per level $+$ Starting points Since Daniel wants to have at least $3100$ points before going to bed, we can set up an inequality. Number of points $\geq 3100$ Levels completed $\times$ Points per level $+$ Starting points $\geq 3100$ We are solving for the number of levels to be completed, so let the number of levels be represented by the variable $x$ We can now plug in: $x \cdot 550 + 140 \geq 3100$ $ x \cdot 550 \geq 3100 - 140 $ $ x \cdot 550 \geq 2960 $ $x \geq \dfrac{2960}{550} \approx 5.38$ Since Daniel won't get points unless he completes the entire level, we round $5.38$ up to $6$ Daniel must complete at least 6 levels.